Identification of Consistent and Inconsistent Academic Achievement in Grouping Units

Background

• The Spike-and-Slab Mixed-Effects Location Scale model (SS-MELSM) methodology identifies clustering units (students, classrooms, etc.) that exhibit unusual levels of residual variability—such as consistency or inconsistency—in academic achievement.

• The Posterior Inclusion Probability (PIP), quantifies the probability that a given random effect is included in the residual variance (scale) model.

• Evidence for retaining the random effect is evidence of unusual variability.

Background

• ivd is a package that facilitates the implementation of the SS-MELSM.

• Once (in)consistent schools are identified, researchers may want to investigate these clusters to understand what distinguishes them from others.

Research question

• The final goal is to enhance the visualizations currently provided by the ivd package.

Method

• Standardized math scores from 11,386 11th and 12th-grade students across 160 schools.

• I will work with posterior estimates from the scale model.

• Specifically, I will use the PIPs, the estimated random effects standard deviations, the within-school residual variance, and the estimated math scores.

Improvements to existing plots

PIP plot

Improvements to existing plots

Funnel plot

Improvements to existing plots

Outcome plot

New plots

Sugarloaf plots